Characterization of the limit load in the case of an unbounded elastic convex

Elyacoubi, Adnene; Hadhri, Taieb

doi:10.1051/m2an:2005028

Elyacoubi, Adnene ; Hadhri, Taieb

ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 4, pp. 637-648.

Résumé

In this work we consider a solid body $Ω \subset ℝ^{3}$ constituted by a nonhomogeneous elastoplastic material, submitted to a density of body forces $λ f$ and a density of forces $λ g$ acting on the boundary where the real $λ$ is the loading parameter. The problem is to determine, in the case of an unbounded convex of elasticity, the Limit load denoted by $\bar{λ}$ beyond which there is a break of the structure. The case of a bounded convex of elasticity is done in [El-Fekih and Hadhri, RAIRO: Modél. Math. Anal. Numér. 29 (1995) 391-419]. Then assuming that the convex of elasticity at the point x of $Ω$ , denoted by K(x), is written in the form of $K^{D} (x) + ℝ I$ , I is the identity of ${ℝ^{9}}_{s y m}$ , and the deviatoric component $K^{D}$ is bounded regardless of x $\in Ω$ , we show under the condition “Rot f $\neq 0$ or g is not colinear to the normal on a part of the boundary of $Ω$ ”, that the Limit Load $\bar{λ}$ searched is equal to the inverse of the infimum of the gauge of the Elastic convex translated by stress field equilibrating the unitary load corresponding to $λ = 1$ ; moreover we show that this infimum is reached in a suitable function space.

DOI : 10.1051/m2an:2005028

Classification : 74xx
Mots clés : elasticity, limit load

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     title = {Characterization of the limit load in the case of an unbounded elastic convex},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {637--648},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {4},
     year = {2005},
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     mrnumber = {2165673},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an:2005028/}
}

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Elyacoubi, Adnene; Hadhri, Taieb. Characterization of the limit load in the case of an unbounded elastic convex. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 4, pp. 637-648. doi : 10.1051/m2an:2005028. http://www.numdam.org/articles/10.1051/m2an:2005028/

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